Look first at ONE single sale. A loaf goes for €100 (a very big loaf — we are keeping round numbers). That sum is three things AT ONCE: output (from wheat to bread, firms created it), expenditure (the customer paid it), and income (it ends up entirely in pockets — wages, production taxes, profits). GDP merely generalises: add up all the final sales in the country, and the same total reads through what is created, through who pays for it, or through who collects it. The identity is no miracle: it is the same money, looked at three times.

We add up value added — for each producer: its sales, plus whatever enters inventory (assumption 3), minus its purchases from other firms (its “intermediate consumption”, as INSEE calls it). Why not turnover? Because the baker's flour already lives inside the miller's: turnovers overlap, value added never does. (A word of rigour: everything is counted NET OF TAX. The VAT paid by the final customer enters nobody's value added — INSEE adds it separately, right at the end, to get back to GDP at the prices actually paid. Above all, hold on to the idea: each value is counted only once.)

Open up a firm's value added: it splits entirely into three. The wages of those who work there; production taxes — the taxes you pay by the very fact of producing, such as property tax on the workshop (nothing to do with corporation tax, levied afterwards on profit); and all the rest: profit — which is also where the pay of a craftsman who draws no wage sits. (National accountants call it “gross operating surplus” for a company — and “mixed income” for a self-employed person, in whom it blends labour and capital. Hold on to “profit”.) Summing these three incomes across the whole country therefore gives back, necessarily, the sum of value added — this is assumption 4 turned into a formula.

Four possible customers, not one more: households (C, for Consumption — all of us, when we buy in order to live), firms (I, for Investment — machines, buildings… and inventories, where the unsold goods of assumption 3 land), the government (G, for Government — its purchases and the wages of its staff, NOT pensions or benefits: there it redistributes, it buys nothing), and abroad (X, for eXports). One single adjustment: C, I and G contain imported products, made elsewhere — so we take out iMports, hence the “X − M” (the course “GDP” goes through each letter). And the identity reads both ways: it lets you recover a missing piece, and serves as a safety rail — two routes that diverge mean an error somewhere. Click each angle of view: